Invited by School of Mathematics and Statistics, Ph.D. Zhong Zheng from Hexi University and Lidan Liao from Nanchang university will give lectures.

Reporter: Zhong Zheng

Title：On Euler-extrapoated double-step scale splitting method for a class of complex symmetric linear systems

Time：2:00 p.m.,Dec. 11th, 2021

Location: Room 631, Polytechnic building

Abstract：We propose an Euler-extrapolated double-step scale splitting (EDSS) iteration method for solving a class of complex symmetric linear systems. Under appropriate constraints, we prove that the EDSS method is unconditionally convergent. Furthermore, we illustrate that the spectral radius of the EDSS iteration matrix does not exceed 0.41057 when the argumentθis2π/45and the relaxation parameterαis 0.27614 or 3.62132, respectively. Numerical experiments verify the correctness of the theoretical results and demonstrate the effectiveness of the EDSS method.

Reporter：Mingli Zeng

Title：Preconditioned iterative method for nonsymmetric saddle point linear systems

Time：3:00 p.m.,Dec. 11th, 2021

Location: Room 631, Polytechnic building

Abstract:In this paper, a new preconditioned iterative method is presented to solve a class of nonsymmetric nonsingular or singular saddle point problems. The implementation of the proposed preconditioned Krylov subspace method avoids solving inverse of Schur complement and only needs to solve one linear sub-system at each step, which implies that it may save considerable costs. Theoretical convergence analysis, including the bounds of eigenvalues and eigenvectors, the degree of the minimal polynomial of the preconditioned matrix, are discussed in details. Moreover, a novel algebraic estimation technique for finding a practical iteration parameter is presented, which is very effective and practical even for large scale problems. At last, some numerical examples are carried, showing that the theoretical results are valid and convincing.